1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nesterboy [21]
3 years ago
13

1) A thin ring made of uniformly charged insulating material has total charge Q and radius R. The ring is positioned along the x

-y plane of a 3d coordinate system such that the center of the ring is at the origin of the coordinate system. (a) Determine an expression for the potential at an arbitrary location along the z-axis in terms of Q, R, and z. (b) Use this expression to determine an expression for the magnitude of the electric field at an arbitrary location along the z-axis in terms of Q, R, and z. Hint: Apply the technique of charge integration in part (a) and poten
Physics
1 answer:
allochka39001 [22]3 years ago
4 0

Answer:

(A) considering the charge "q" evenly distributed, applying the technique of charge integration for finite charges, you obtain the expression for the potential along any point in the Z-axis:

V(z)=\frac{Q}{4\pi (\epsilon_{0}) \sqrt{R^{2} +z^{2}}  }

With (\epsilon_{0}) been the vacuum permittivity

(B) The expression for the magnitude of the E(z) electric field along the Z-axis is:

E(z)=\frac{QZ}{4\pi (\epsilon_{0}) (R^{2} +z^{2})^{\frac{3}{2} }    }

Explanation:

(A) Considering a uniform linear density λ_{0} on the ring, then:

dQ=\lambda dl (1)⇒Q=\lambda_{0} 2\pi R(2)⇒\lambda_{0}=\frac{Q}{2\pi R}(3)

Applying the technique of charge integration for finite charges:

V(z)= 4\pi (ε_{0})\int\limits^a_b {\frac{1}{ r'  }} \, dQ(4)

Been r' the distance between the charge and the observation point and a, b limits of integration of the charge. In this case a=2π and b=0.

Using cylindrical coordinates, the distance between a point of the Z-axis and a point of a ring with R radius is:

r'=\sqrt{R^{2} +Z^{2}}(5)

Using the expressions (1),(4) and (5) you obtain:

V(z)= 4\pi (\epsilon_{0})\int\limits^a_b {\frac{\lambda_{0}R}{ \sqrt{R^{2} +Z^{2}}  }} \, d\phi

Integrating results:

V(z)=\frac{Q}{4\pi (\epsilon_{0}) \sqrt{R^{2} +z^{2}}  }   (S_a)

(B) For the expression of the magnitude of the field E(z), is important to remember:

|E| =-\nabla V (6)

But in this case you only work in the z variable, soo the expression (6) can be rewritten as:

|E| =-\frac{dV(z)}{dz} (7)

Using expression (7) and (S_a), you get the expression of the magnitude of the field E(z):

E(z)=\frac{QZ}{4\pi (\epsilon_{0}) (R^{2} +z^{2})^{\frac{3}{2} }    } (S_b)

You might be interested in
If Spacecraft X has twice the mass of Spacecraft Y , then what is true about X and Y ?
Solnce55 [7]

I don't know what you were trying to copy or type in Choice-E .

All three statements are true, so the answer should say "I, II, and III".

6 0
3 years ago
An unknown element is found to have two naturally occurring isotopes, 200X and 210X with atomic masses of 200.028 and 210.039 re
Kruka [31]

Answer:

The average atomic mass of X is 206.0346

Explanation:

Atomic mass of 200X = 200.028

% abundance of 200X = 40% = 40/100 = 0.4

Atomic mass of 210X = 210.039

% abundance of 210X = 100% - 40% = 60% = 60/100 = 0.6

Average atomic mass of X = (0.4×200.028) + (0.6×210.039) = 80.0112 + 126.0234 = 206.0346

5 0
3 years ago
Radiant energy travels in straight lines until it strikes an object where it can be ______,_____or transmitted
Alborosie
<span>Radiant energy travels in straight lines until it strikes an object where it can be absorbed, reflected or transmitted</span>
7 0
3 years ago
Who would be most likely to analyze a tablet with cuneiform to determine what goods were traded by the merchants of Ur?
mars1129 [50]
 I think your answer would Be A. Because historians mostly study written documents, while archaeologists uncover fossils and buildings.
5 0
3 years ago
Read 2 more answers
A rectangular block floats in pure water with 0.400 in. above the surface and 1.60 in. below the surface. When placed in an aque
labwork [276]

Answer:

specific gravity = 0.8

specific gravity of  solution  = 2

Explanation:

given data

rectangular block above water  = 0.400 in

rectangular block below water = 1.60 in

material floats below water = 0.800 in

solution

first we get here specific gravity of block  that is

specific gravity = block vol below ÷ total block vol × specific gravity  water   ..............1

put here value we get

specific gravity =  \frac{1.60}{1.60+0.400}  × 1

specific gravity = 0.8

and now we get here specific gravity of  solution  that is express as

specific gravity of  solution  = total block vol ÷ block vol below × specific gravity  block   ........................2

put here value we get

specific gravity of  solution  = \frac{1.60+0.400}{0.800} × 0.8

specific gravity of  solution  = 2

6 0
3 years ago
Other questions:
  • On a hot summer day, you turn the thermostat in your house way down. Assume that your house is well sealed and that no air enter
    13·1 answer
  • 2.What is forensic paleontology?<br> 4.What are Forensic wood anatomists?
    6·1 answer
  • Does Sun burn? If yes, it burns without Oxygen?
    13·2 answers
  • a kid jumping on a trampoline reaches a height of 0.925m. what was his speed when he left the trampoline?
    10·1 answer
  • How do find the force of buoyancy ​
    12·1 answer
  • The position vector of a particle of mass 2 kg is given as a function of time by ~r = (5 m) ˆı + (5 m/s)t ˆ . Determine the mag
    10·1 answer
  • answers If visible light and radio waves are both examples of electromagnetic waves, why can’t we see radio waves?
    9·1 answer
  • If the impulse is 12 newton . seconds and the force is 5 newtons, how long<br> did the force act?
    6·1 answer
  • Driving to work one morning, you get a flat tire. When using the car jack, you apply 120N of force to the jack and the jack in t
    6·1 answer
  • How are loudness and intensity related to the amplitude and energy of a sound wave? What is the unit of intensity?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!